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The divergence problem, which manifests as an unstable response relationship between tree-ring growth and climatic factors under the background of global warming, poses a challenge to both the traditional theory of dendroclimatology and the reliability of climatic reconstructions based on tree-ring data. Although Schrenk spruce, as the dominant tree species in the Tianshan Mountains, is frequently applied in the dendrochronological studies, the understanding of the divergence problem of this tree species is still limited. This study conducted correlation analysis between climatic factors and tree-ring width chronologies from 51 living and healthy specimens of Schrenk spruce at sites of high and low elevation in the Alatau Mountains to determine the stability of the response. The results revealed that the tree-ring width of the spruce specimens was correlated positively with precipitation and correlated negatively with temperature. Although the variations of the two tree-ring chronologies were similar, the radial growth of the spruce at the low elevation was found more sensitive to climatic factors. Furthermore, the sensitivity of tree growth to climate demonstrated an obvious increase after an abrupt change of climate under the background of the recent warming and wetting trend. Increased drought stress, calculated based on climatic data, was regarded as the main reason for this phenomenon. The results supply the gap of the stability of climatic response of tree growth in Central Asia to some extent.